Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential Question
How can I use a proportion to increase or decrease the size of an image or quantity?
= NOTE=
You have know your end label first
Unit rate: numerator/denominator and add label. e.g. miles/gallon>>gallon of gas used for x miles
Inverse mathematics
Investigation 3.3: Sharing Pizza
On the last day of camp, the cook served pizza. The camp dining room has two kinds of tables. A large table seats 10 people, and a small table seats 8 people. The cook tells the students who are serving dinner to put four pizzas on each large table and three pizzas on each small table.
Problem 3.3
A. If the pizzas at a table are shared equally by everyone at the table, will a person sitting at a small table get the same amount of pizza as a person sitting at a large table? Explain your reasoning.
ANS: No, because the people sit at the large table gets more pizza than small tables.
> Large table = 4/10 = 0.4 pizza/person
Small table = 3/8 = 0.375 pizza/person
B. The ratio of large tables to small table is 8 to 5. There are exactly enough seats for 240 campers. How many tables of each kind are there?
ANS: 8 to 5
> 8*10 to 5*8
> 80 to 40
> 80*2:40*2
>160:80 (Number of campers)
- Large table
160/10 = 16
Small table
80/8 = 10
Problem 3.3 Follow-up
1. How were ratios helpful in thinking about the problem?
ANS: Ratios were helpful in thinking about the problem since it provided a clear distinction between the two data.
2. How many pizzas will the cook need to make in order to put 4 pizzas on each large table and 3 pizzas in each small table?
ANS: Large table = 16*4 = 64
Small table = 10*3 = 30
- So the cook will need to make 64+30=94 pizzas to put 4 pizzas on each large table and 3 pizzas in each small table.
January 24th, 2011
C.L.
Big Idea
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential Question
How can I use a proportion to increase or decrease the size of an image or quantity?
=
NOTE=
You have know your end label first
Unit rate: numerator/denominator and add label. e.g. miles/gallon>>gallon of gas used for x miles
Inverse mathematics
Investigation 3.3: Sharing Pizza
On the last day of camp, the cook served pizza. The camp dining room has two kinds of tables. A large table seats 10 people, and a small table seats 8 people. The cook tells the students who are serving dinner to put four pizzas on each large table and three pizzas on each small table.
Problem 3.3
A. If the pizzas at a table are shared equally by everyone at the table, will a person sitting at a small table get the same amount of pizza as a person sitting at a large table? Explain your reasoning.
ANS: No, because the people sit at the large table gets more pizza than small tables.
> Large table = 4/10 = 0.4 pizza/person
Small table = 3/8 = 0.375 pizza/person
B. The ratio of large tables to small table is 8 to 5. There are exactly enough seats for 240 campers. How many tables of each kind are there?
ANS: 8 to 5
> 8*10 to 5*8
> 80 to 40
> 80*2:40*2
>160:80 (Number of campers)
- Large table
160/10 = 16
Small table
80/8 = 10
Problem 3.3 Follow-up
1. How were ratios helpful in thinking about the problem?
ANS: Ratios were helpful in thinking about the problem since it provided a clear distinction between the two data.
2. How many pizzas will the cook need to make in order to put 4 pizzas on each large table and 3 pizzas in each small table?
ANS: Large table = 16*4 = 64
Small table = 10*3 = 30
- So the cook will need to make 64+30=94 pizzas to put 4 pizzas on each large table and 3 pizzas in each small table.